Symmetries of the Celestial Supersphere

Abstract: We study the celestial CFT dual to theories with bulk supersymmetry. The boundary theory realizes supersymmetry in the spirit of the Green-Schwarz superstring: there is manifest 4d super-Poincar\'e symmetry, but no 2d superconformal symmetry. Nevertheless, we can extend the celestial sphere itself to a supermanifold -- the celestial supersphere. This provides a unified framework for describing key features of celestial holography, including conformally soft theorems, OPEs, and chiral soft algebras. Using these tools, we demonstrate that the $\frak{bms}{4}$ algebra extends to a novel $\frak{sbms}{4|\mathcal{N}}$ algebra. We also relate the supersymmetric $L(w_{1+\infty}^\wedge)$ algebra to Hamiltonian vector fields on $\mathbb{C}^{2|\mathcal{N}}$, consistent with the expectation from twistor theory, and deduce the deformation of this algebra by a cosmological constant, $\Lambda$. These results are all universal and independent of the specific details of the underlying theory.